Nuprl Lemma : rng_of_alg_wf
∀A:Type. ∀a:algebra_sig{i:l}(A). (a↓rg ∈ RngSig)
Proof
Definitions occuring in Statement :
rng_of_alg: a↓rg,
algebra_sig: algebra_sig{i:l}(A),
all: ∀x:A. B[x],
member: t ∈ T,
universe: Type,
rng_sig: RngSig
Definitions unfolded in proof :
rng_of_alg: a↓rg,
rng_sig: RngSig,
all: ∀x:A. B[x],
member: t ∈ T
Lemmas referenced :
alg_car_wf,
alg_eq_wf,
alg_le_wf,
alg_plus_wf,
alg_zero_wf,
alg_minus_wf,
alg_times_wf,
alg_one_wf,
alg_div_wf,
unit_wf2,
bool_wf,
algebra_sig_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
lambdaFormation,
cut,
dependent_pairEquality,
lemma_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
cumulativity,
hypothesisEquality,
hypothesis,
because_Cache,
functionEquality,
unionEquality,
productEquality,
universeEquality
Latex:
\mforall{}A:Type. \mforall{}a:algebra\_sig\{i:l\}(A). (a\mdownarrow{}rg \mmember{} RngSig)
Date html generated:
2016_05_16-AM-07_26_19
Last ObjectModification:
2015_12_28-PM-05_08_20
Theory : algebras_1
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