Nuprl Lemma : oob-getleft_wf

`∀[B,A:Type]. ∀[x:{x:one_or_both(A;B)| ↑oob-hasleft(x)} ].  (oob-getleft(x) ∈ A)`

Proof

Definitions occuring in Statement :  oob-getleft: `oob-getleft(x)` oob-hasleft: `oob-hasleft(x)` one_or_both: `one_or_both(A;B)` assert: `↑b` uall: `∀[x:A]. B[x]` member: `t ∈ T` set: `{x:A| B[x]} ` universe: `Type`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` oob-getleft: `oob-getleft(x)` all: `∀x:A. B[x]` implies: `P `` Q` bool: `𝔹` unit: `Unit` it: `⋅` btrue: `tt` uiff: `uiff(P;Q)` and: `P ∧ Q` uimplies: `b supposing a` ifthenelse: `if b then t else f fi ` bfalse: `ff` subtype_rel: `A ⊆r B` top: `Top` prop: `ℙ` so_lambda: `λ2x.t[x]` so_apply: `x[s]` oob-hasleft: `oob-hasleft(x)` or: `P ∨ Q` not: `¬A` false: `False`
Lemmas referenced :  oobleft?_wf bool_wf eqtt_to_assert oobleft-lval_wf uiff_transitivity equal-wf-T-base assert_wf bnot_wf not_wf eqff_to_assert assert_of_bnot pi1_wf_top oobboth-bval_wf top_wf oob-subtype equal_wf set_wf one_or_both_wf oob-hasleft_wf assert_of_bor oobboth?_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut setElimination thin rename sqequalRule extract_by_obid sqequalHypSubstitution isectElimination cumulativity hypothesisEquality hypothesis lambdaFormation unionElimination equalityElimination because_Cache productElimination independent_isectElimination equalityTransitivity equalitySymmetry baseClosed independent_functionElimination applyEquality lambdaEquality isect_memberEquality voidElimination voidEquality dependent_functionElimination axiomEquality universeEquality

Latex:
\mforall{}[B,A:Type].  \mforall{}[x:\{x:one\_or\_both(A;B)|  \muparrow{}oob-hasleft(x)\}  ].    (oob-getleft(x)  \mmember{}  A)

Date html generated: 2018_05_21-PM-08_00_02
Last ObjectModification: 2017_07_26-PM-05_36_53

Theory : general

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