Nuprl Lemma : sq_stable__grp_leq
∀[g:GrpSig]. ∀[a,b:|g|]. SqStable(a ≤ b)
Proof
Definitions occuring in Statement :
grp_leq: a ≤ b,
grp_car: |g|,
grp_sig: GrpSig,
sq_stable: SqStable(P),
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
grp_leq: a ≤ b,
uall: ∀[x:A]. B[x],
member: t ∈ T,
infix_ap: x f y,
implies: P ⇒ Q,
all: ∀x:A. B[x],
sq_stable: SqStable(P),
prop: ℙ
Lemmas referenced :
sq_stable_from_decidable,
assert_wf,
grp_le_wf,
decidable__assert,
assert_witness,
squash_wf,
grp_car_wf,
grp_sig_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
applyEquality,
hypothesisEquality,
hypothesis,
independent_functionElimination,
dependent_functionElimination,
lambdaEquality,
because_Cache,
isect_memberEquality
Latex:
\mforall{}[g:GrpSig]. \mforall{}[a,b:|g|]. SqStable(a \mleq{} b)
Date html generated:
2016_05_15-PM-00_11_47
Last ObjectModification:
2015_12_26-PM-11_43_25
Theory : groups_1
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