Nuprl Lemma : comb_for_grp_lt_wf
λg,a,b,z. (a < b) ∈ g:GrpSig ⟶ a:|g| ⟶ b:|g| ⟶ (↓True) ⟶ ℙ
Proof
Definitions occuring in Statement :
grp_lt: a < b,
grp_car: |g|,
grp_sig: GrpSig,
prop: ℙ,
squash: ↓T,
true: True,
member: t ∈ T,
lambda: λx.A[x],
function: x:A ⟶ B[x]
Definitions unfolded in proof :
member: t ∈ T,
squash: ↓T,
uall: ∀[x:A]. B[x],
prop: ℙ
Lemmas referenced :
grp_lt_wf,
squash_wf,
true_wf,
grp_car_wf,
grp_sig_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaEquality,
sqequalHypSubstitution,
imageElimination,
cut,
lemma_by_obid,
isectElimination,
thin,
hypothesisEquality,
equalityTransitivity,
hypothesis,
equalitySymmetry
Latex:
\mlambda{}g,a,b,z. (a < b) \mmember{} g:GrpSig {}\mrightarrow{} a:|g| {}\mrightarrow{} b:|g| {}\mrightarrow{} (\mdownarrow{}True) {}\mrightarrow{} \mBbbP{}
Date html generated:
2016_05_15-PM-00_11_54
Last ObjectModification:
2015_12_26-PM-11_42_59
Theory : groups_1
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