`∀[c,d,t,t':ℤ].  uiff((c + t) ≤ (d + t');c ≤ d) supposing t = t' ∈ ℤ`

Proof

Definitions occuring in Statement :  uiff: `uiff(P;Q)` uimplies: `b supposing a` uall: `∀[x:A]. B[x]` le: `A ≤ B` add: `n + m` int: `ℤ` equal: `s = t ∈ T`
Definitions unfolded in proof :  uiff: `uiff(P;Q)` and: `P ∧ Q` uimplies: `b supposing a` member: `t ∈ T` le: `A ≤ B` not: `¬A` implies: `P `` Q` false: `False` prop: `ℙ` uall: `∀[x:A]. B[x]` sq_type: `SQType(T)` all: `∀x:A. B[x]` guard: `{T}` subtype_rel: `A ⊆r B` top: `Top`
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity independent_pairFormation isect_memberFormation introduction cut sqequalRule sqequalHypSubstitution productElimination thin independent_pairEquality lambdaEquality dependent_functionElimination hypothesisEquality because_Cache axiomEquality lemma_by_obid isectElimination addEquality hypothesis voidElimination equalityTransitivity equalitySymmetry intEquality isect_memberEquality instantiate cumulativity independent_isectElimination independent_functionElimination minusEquality baseApply closedConclusion baseClosed applyEquality voidEquality natural_numberEquality

Latex:
\mforall{}[c,d,t,t':\mBbbZ{}].    uiff((c  +  t)  \mleq{}  (d  +  t');c  \mleq{}  d)  supposing  t  =  t'

Date html generated: 2016_05_13-PM-03_31_19
Last ObjectModification: 2016_01_14-PM-06_41_22

Theory : arithmetic

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