Proof

Definitions unfolded in proof :  uall: [x:A]. B[x] uimplies: supposing a member: t ∈ T int_upper: {i...} uiff: uiff(P;Q) and: P ∧ Q rev_uimplies: rev_uimplies(P;Q) pa-add: pa-add(p;x;y) all: x:A. B[x] nat_plus: + decidable: Dec(P) or: P ∨ Q not: ¬A implies:  Q satisfiable_int_formula: satisfiable_int_formula(fmla) exists: x:A. B[x] false: False prop: iff: ⇐⇒ Q basic-padic: basic-padic(p) bpa-equiv: bpa-equiv(p;x;y) bpa-add: bpa-add(p;x;y) cand: c∧ B rev_implies:  Q nat: ge: i ≥  has-value: (a)↓ le: A ≤ B guard: {T} true: True squash: T subtype_rel: A ⊆B
Lemmas referenced :  equal-padics pa-add_wf bpa-equiv-iff-norm bpa-add_wf int_upper_properties decidable__lt full-omega-unsat intformand_wf intformnot_wf intformless_wf itermConstant_wf itermVar_wf intformle_wf istype-int int_formula_prop_and_lemma int_formula_prop_not_lemma int_formula_prop_less_lemma int_term_value_constant_lemma int_term_value_var_lemma int_formula_prop_le_lemma int_formula_prop_wf istype-less_than imax_ub nat_properties decidable__le istype-le value-type-has-value int-value-type imax_wf fastexp_wf subtract_wf itermSubtract_wf int_term_value_subtract_lemma bpa-equiv_wf basic-padic_wf istype-int_upper imax_nat intformeq_wf int_formula_prop_eq_lemma p-adics_wf p-int_wf exp_wf2 p-mul_wf p-add_wf equal_wf squash_wf true_wf istype-universe p-distrib nat_plus_wf p-mul-assoc exp-fastexp p-mul-int subtype_rel_self exp_add iff_weakening_equal itermAdd_wf int_term_value_add_lemma istype-nat decidable__equal_int
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation_alt cut introduction extract_by_obid sqequalHypSubstitution isectElimination thin setElimination rename because_Cache hypothesis hypothesisEquality productElimination independent_isectElimination dependent_functionElimination dependent_set_memberEquality_alt natural_numberEquality unionElimination approximateComputation independent_functionElimination dependent_pairFormation_alt lambdaEquality_alt int_eqEquality Error :memTop,  sqequalRule independent_pairFormation universeIsType voidElimination inlFormation_alt inrFormation_alt callbyvalueReduce intEquality inhabitedIsType lambdaFormation_alt equalityTransitivity equalitySymmetry applyLambdaEquality equalityIstype productIsType applyEquality imageElimination imageMemberEquality baseClosed instantiate universeEquality addEquality hyp_replacement

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