Nuprl Lemma : decidable__lt
∀i,j:ℤ. Dec(i < j)
Proof
Definitions occuring in Statement :
less_than: a < b,
decidable: Dec(P),
all: ∀x:A. B[x],
int: ℤ
Definitions unfolded in proof :
less_than: a < b,
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
member: t ∈ T,
prop: ℙ,
implies: P ⇒ Q,
decidable: Dec(P),
or: P ∨ Q,
and: P ∧ Q,
cand: A c∧ B
Lemmas referenced :
decidable__squash,
and_wf,
less_than'_wf,
member_wf,
decidable__and,
decidable__less_than',
not_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
lambdaFormation,
cut,
lemma_by_obid,
hypothesis,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
intEquality,
independent_functionElimination,
dependent_functionElimination,
inlFormation,
independent_pairFormation
Latex:
\mforall{}i,j:\mBbbZ{}. Dec(i < j)
Date html generated:
2016_05_13-PM-03_20_00
Last ObjectModification:
2015_12_26-AM-09_09_21
Theory : sqequal_1
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