Nuprl Lemma : comb_for_rng_nat_op_wf
λr,n,u,z. (n ⋅r u) ∈ r:Rng ⟶ n:ℕ ⟶ u:|r| ⟶ (↓True) ⟶ |r|
Proof
Definitions occuring in Statement :
rng_nat_op: n ⋅r e,
rng: Rng,
rng_car: |r|,
nat: ℕ,
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,
rng: Rng
Lemmas referenced :
rng_nat_op_wf,
squash_wf,
true_wf,
rng_car_wf,
nat_wf,
rng_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaEquality,
sqequalHypSubstitution,
imageElimination,
cut,
lemma_by_obid,
isectElimination,
thin,
hypothesisEquality,
equalityTransitivity,
hypothesis,
equalitySymmetry,
setElimination,
rename
Latex:
\mlambda{}r,n,u,z. (n \mcdot{}r u) \mmember{} r:Rng {}\mrightarrow{} n:\mBbbN{} {}\mrightarrow{} u:|r| {}\mrightarrow{} (\mdownarrow{}True) {}\mrightarrow{} |r|
Date html generated:
2016_05_15-PM-00_26_49
Last ObjectModification:
2015_12_26-PM-11_59_29
Theory : rings_1
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